Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T09:23:38.398Z Has data issue: false hasContentIssue false
  • English
  • Français

Fixed point theorems in H-spaces and equilibrium points of abstract economies

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  09 April 2009

E. Tarafdar
E. Tarafdar
Affiliation:
University of QueenslandSt. Lucia 4072, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Some fixed point theorems on H-spaces are presented. These theorems are then applied to generalize a theorem of Fan concerning sets with convex sections to H-spaces and to prove the existence of equilibrium points of abstract economics in which the commodity space is an H-space.

MSC classification

Secondary: 47H10: Fixed-point theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 2 , October 1992 , pp. 252 - 260
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Bewley, T. G., ‘Existence of equilibria in economics with infinitely many commodities’, J. Economic Theory 4 (1972), 514–540.CrossRefGoogle Scholar
[2]Debreu, G., ‘A social equilibrium existence theorem’, Proc. National Academy of Sciences, U.S.A. 38 (1952) 886–893.Google Scholar
[3]Fan, K., ‘Some properties of convex sets related to fixed point theorems’, Math. Annal. 266 (1984) 519–537.CrossRefGoogle Scholar
[4]Gale, D. and Mas-Colell, A., ‘An equilibrium existence for a general model without ordered preferences’, J. Math. Economics 2 (1975), 9–15.CrossRefGoogle Scholar
[5]Horvath, C., ‘Point fixes et coincidences pour les applications multivoques sans convexite’, C. R. Acad. Sci. Paris 296 (1983), 403–406.Google Scholar
[6]Horvath, C., ‘Point fixes et coincidences dans les espaces topologiques compacts contractiles’, C.R. Acad. Sci. Paris 299 (1984), 519–521.Google Scholar
[7]Horvath, C., ‘Some results on multivalued mappings and inequalities without convexity’, in Nonlinear and Convex Analysis, (Eds. Lin, B. L. and Simons, S.), Marcel Dekker, 1987, pp. 99–106.Google Scholar
[8]Nash, J. F., ‘Equilibrium points in N-person games’, Proc. National Academy of Sciences U.S.A. 36 (1950), 48–59.CrossRefGoogle ScholarPubMed
[9]Shafer, W. and Sonnenschein, H., ‘Equilibrium in abstract economics without ordered preferences’, J. Math. Economics 2 (1975), 345–348.CrossRefGoogle Scholar
[10]Tarafdar, E., ‘A fixed point theorem and equilibrium point of an abstract economy’, to appear in J. Math. Economics.Google Scholar
[11]Tarafdar, E., ‘On nonlinear variational inequalities’, Proc. Amer. Math. Soc. 67 (1977), 95–98.CrossRefGoogle Scholar
[12]Tarafdar, E., ‘A fixed point theorem in H-space and related results’, Bull. Austral. Math. Soc. 42 (1990), 133–140.CrossRefGoogle Scholar
[13]Tarafdar, E., ‘On two theorems concerning sets with convex sections’, Bull. Austral. Math. Soc. 38 (1988), 397–400.CrossRefGoogle Scholar